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%I #33 Sep 10 2023 01:53:03
%S 0,0,1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,12,12,13,14,14,15,16,16,17,18,19,
%T 19,20,21,21,22,23,24,24,25,26,26,27,28,28,29,30,31,31,32,33,33,34,35,
%U 36,36,37,38,38,39,40,41,41,42,43,43,44,45,45,46,47
%N a(n) = floor(n/sqrt(2)).
%C For n > 0: A006337(n) = number of repeating n's. - _Reinhard Zumkeller_, Jul 04 2015
%H Vincenzo Librandi, <a href="/A049472/b049472.txt">Table of n, a(n) for n = 0..10000</a>
%H Robbert Fokkink, <a href="https://arxiv.org/abs/2309.01644">The Pell Tower and Ostronometry</a>, arXiv:2309.01644 [math.CO], 2023.
%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%p A049472:=n->floor(n/sqrt(2)): seq(A049472(n), n=0..100); # _Wesley Ivan Hurt_, Jun 25 2016
%t Floor[Range[0,70]/Sqrt[2]] (* _Harvey P. Dale_, Aug 22 2011 *)
%o (Magma) [Floor(n/Sqrt(2)): n in [0..70] ]; // _Vincenzo Librandi_, Aug 23 2011
%o (Haskell)
%o a049472 = floor . (/ sqrt 2) . fromIntegral
%o -- _Reinhard Zumkeller_, Jul 04 2015
%o (PARI) a(n)=sqrtint(n^2\2) \\ _Charles R Greathouse IV_, Sep 02 2015
%Y First differences give A080764.
%Y Cf. A006337, A049474.
%K nonn,easy
%O 0,4
%A _Thomas Kellar_
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